I'm throwing in my two cents.
There's something key here. The Assailant naturally kills quicker than an Illum one on one. What you're seeing imo is the effects of shield mitigation. The Assailant is undoutably doing more damage because ALL of it's damage is in the phase missile. The Illuminator is doing less damage because only roughly 60% of the damage is in the front beam, so the shield mitigation won't go up as fast, meaning less of the beam's damage is negated.
The phase missile's damage is negated because it does more damage than the beam which makes the mitigation climb like crazy. Since the higher rate of damage doesn't stop, the mitigation actually goes up to 57% negated.
So an unupgraded Assailant does 13 dps - 57% = 5.6 dps.
An Illum does roughly 10 dps with the front beam and only goes through 15-25% shield mitigation as mentioned by Howthe. That makes the Illum do on average 8 dps-ish.
If I recall the Illum has more health and shields than an Assailant?
I'm not surprised that the Illum won in both cases.
Ok, for fully upped phase missiles, I think you're seeing the same thing. It makes sense that it would be closer, but the fact is Assailants are Tier One. The tradeoff with them is that you get them earlier in exchange for the worst STARTING long range frigate. I believe Assailants are the best LRF fully upgraded. If you don't, ask the Vasari player who can knock out ur level 10 cap and fully upped in health and armor Starbase with ease.
Also, it's worth noting that the Assailant is going to be the most frail LRF of the three b/c of the Tier one accessibility. The tradeoff is you get them early and can upgrade them as much as you like. Vasari Armor absolutely rocks (Get up to Tier 4 and you up by 4 armor, VERY POWERFUL)
The Illum still needs to be toned down a little BUT ONLY A LITTLE. I'd like to see them get a reduction to 1 Armor and say ballpark -50 points in health and shields. Make them frail so they can't stand alone. They do their job. They're fleet destroyers. They just need to be less beefy so the damn counters don't have as hard a time as they do now.
Scouts fend off Illums easily early. In late game, HC's do it well enough. Repulse can make things extremely unfair, but that's a different problem in it's own. (For the love of pete make Repulse cost more antimatter, like 15-25 aps. That's fair. 8 Guardians would still be able to abuse it, but not forever like people do now)